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C(X) can sometimes determine X without X being realcompact
Published in Charles University, Faculty of Mathematics and Physics
Volume: 46
Issue: 4
Pages: 711 - 720
As usual C(X) will denote the ring of real-valued continuous functions on a Tychonoff space X. It is well-known that if X and Y are realcompact spaces such that C(X) and C(Y ) are isomorphic, then X and Y are homeomorphic; that is C(X) determines X. The restriction to realcompact spaces stems from the fact that C(X) and C(νX) are isomorphic, where uX is the (Hewitt) realcompactification of X. In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact spaces is exhibited such that C(X) determines X. The problem of getting similar results for other restricted classes of generalized realcompact spaces is posed. © 2005 Charles University, Faculty of Mathematics and Physics.
About the journal
JournalCommentationes Mathematicae Universitatis Carolinae
PublisherCharles University, Faculty of Mathematics and Physics